How does the Cloth Stiffness Scaling option work?
Cloth Stiffness Scaling 

Q: How does Cloth Stiffness Scaling work? 

A: Basically, you just (1) Create a Vector Group from the Plane, (2) Weight Paint each half of the Plane red/blue, (3) Then set the min&amp;max values for Bending stiffness to 0.0001&amp;1000.0. You can test it with a cloth falling over a collision sphere. The following post aims to elaborate on this explanation.



Feature Functionality

According to the Documentation for Blender 2.4, the Stiffness Scaling feature allows a vertex group to have a different bending/structural stiffness value for each vertex within the vertex group (as opposed to the same bending/structural stiffness value for each vertex). This requires working with "Vertex Groups" and "Weight Paint" features.

Blender 2.4 Docs: 
http://wiki.blender.org/index.php/Doc:2.4/Reference/Panels/Object/Physics/Cloth#Stiffness_Scaling



Same Stiffness Values

The usual way to apply (bending/structural) stiffness values to a vertex group (or a plane mesh), is to apply a "Cloth" Modifier to a Plane Mesh (hopefully, well subdivided) via the "Modifiers > Add Modifier" Panel. Once the Cloth Modifier is applied to the Plane Mesh, then you can set the "Structural" and "Bending" stiffness values via the "Physics > Cloth" Panel. For example, you can set "Bending" to 0.0001 to be very silky, or you can set "Bending" to 1000.00 to be very leathery. Now all of the vertices within the Plane Mesh will have the same stiffness values.



Different Stiffness Values

Now, let's say that we want each of the vertices (of the Plane Mesh) to have a different structural/bending stiffness value. In this example, we want the left half of the cloth to have 1000.0 "Bending" stiffness and the right half of the cloth to have 0.0001 "Bending" stiffness (aka, leathery on the left and silky on the right). To do this, we will need to work with the "Vertex Groups", "Weight Paint", and "Cloth Stiffness Scaling" features.

First, we want to group all of the vertices from the Plane Mesh into a Vertex Group. To do this, we "add a new vertex group to the active object" via the "Data > Vertex Groups" panel (in this case, the active object should be the Plane Mesh). Once the new Vertex Group is created, it should have a default name of "Group". Feel free to re-name it to anything you want -- I will rename it to "Cloth_Group_001". Now, we've created our Vertex Group! Great Job!



Second, we need to Weight Paint the Vertex Group of the Plane Mesh (aka, "Cloth_Group_001"). Weight Paint controls can be accessed by changing "Object Mode" (or "Edit Mode") to "Weight Paint". Now, you will be controlling an interactive brush with a "Weight" between 0.000 to 1.000, a "Radius" between 1 to 200 pixels, and a "Strength" between 0.000 and 1.000. Paint the left half of the Plane Mesh to Red (aka, Weight=1.0), and paint the right half of the Plane Mesh to Blue (aka, Weight=0.0). ((I suggest using a Strength of 1.0, and choosing an Radius Size that is comfortable for you)). Now, you should see the left half colored Red and the right half colored Blue. You've just Weight Painted the vertices in your Vertex Group (of the Plane Mesh)! Great job!



Finally, we can go back to our "Physics > Cloth" and "Physics > Cloth Stiffness Scaling" panels. Using these Cloth panels, we are going to set the minimum value for "Stiffness Scaling" and we are going to set the maximum value for "Stiffness Scaling". We first need to enable "Cloth Stiffness Scaling" via "Physics > Cloth Stiffness Scaling" panel. Now that stiffness scaling is enabled, we want to set a minimum and maximum value for our "Bending" stiffness values for "Cloth_Group_001" (note: we can do the same thing for our "Structural" stiffness values, but this example will only demonstrate the min and max for "Bending" stiffness values). To set the maximum value for our "Bending" stiffness, we need to select "Cloth_Group_001" from the dropdown-menu under "Physics > Cloth Stiffness Scaling > Bending Stiffness:" and then set the max-value for the "Bending Stiffness" to be 1000.0 (you can set this to anything you want, we will use 1000.0 in this example). At this point, be sure that you did both: set the Vertex Group and set the Bending Stiffness "Max:". The last thing you need to do in this section is set the minimum value. To do this, we need go to the "Physics > Cloth" panel and set "Bending:" to 0.0001 (this will serve as the minimum bending value, whenever "Cloth Stiffness Scaling" is enabled --  which you already enabled earlier). You have now set the min and max values for the Vertex Group's Bending Stiffness (Remember that the Vertex Group of your Plane Mesh is re-named to "Cloth_Group_001" for this example). Great job!



To conclude, let's try to understand what we just did. We basically set the Red-Painted vertices to 1000.0 and the Blue-Painted to 0.0001. This is because 1000.0 (maximum) maps to the "Weight"=1.0 from the "Weight Paint" earlier; similarly, 0.0001 (minimum) maps to the "Weight"=0.0. Note that anything that is painted between Red or Blue (e.g., Green/Yellow/Orange) has a Weight in between 0.0 and 1.0; this means that Green/Yellow/Orange will have a Bending Stiffness between 0.0001 (minimum) and 1000.0 (maximum). In our case, we should only have the left half of the vertices painted Red and the right half of the vertices painted Blue; this means that the left half of the vertices have a Bending Stiffness of 1000.0 and the right half of the vertices have a Bending Stiffness of 0.0001.

That's it! Now you have each vertex with a different stiffness value. 

(Note: If you want to change the stiffness for every single vertex in your cloth, just use a different Weight value for each vertex while "Weight Painting".)



Testing

You can take my word that this works, but I'm sure you're eager to see it work for yourself. I would add a Sphere under the Cloth, and add a Collision Modifier to it. Have the Cloth (aka, Plane Mesh) above the Sphere so that when you begin Simulating/Animating it will fall under the force of Gravity and drape the Sphere. Remember to have "Cloth Collision" enabled via the "Physics > Cloth Collision" panel (optional: feel free to enable "Self Collision" as well). 

Now, you can press the "Play Animation" button (towards the bottom of the Blender UI) and see the results of the Cloth falling over a Sphere and draping it. You will notice two (2) things: 


The right half of the cloth will want to hug/engulf/fit the sphere, since the right half of the Vertex Group is silkier ("Bending"=0.0001).
The left half of the cloth will want to try to "spring" back into a planar shape and definitely NOT hug/engulf/fit the sphere as tightly as the other half. (Aka, the cloth will be very stiff in this half; "Bending"=1000.0).


(Note: I've tested Cloth Stiffness Scaling with Blender 2.74, and it works perfectly.)



Conclusion

In conclusion, you will have a very stiff left half (due to the RED paint) and an extremely low stiffness on the right half (due to the BLUE paint).



Does this make sense? Any questions, comments, or feedback are welcome.



References

This link explains one user's struggle and eventual understanding of the Stiffness Scaling feature: https://developer.blender.org/T39371 . Feel free to open the "ClothStiffness2.blend" file referenced in the link, so that you can see a Blender Scene similar to the one example referred to above.